Will StackOverflow discourage creation of two accounts with one used for personal use and another for job use? Also, what if my co-workers 'mess' with me on stackoverflow?
As long as both accounts are kept 'arms length' from each other, you shouldn't have a problem. However, the moment one account gets involved in voting up and down for the benefit of another account, you've crossed a line.
I think that as long as the two never 'meet', it would be ok.
EDIT: By never meet I mean: definitely never vote up each other's questions, and preferably don't even answer each other's questions.
If this is just for asking the occasional 'sensitive' question, just logging in anonymously would probably suffice.
There's nothing wrong per se with multiple accounts (see this question), but you must be careful of "sock puppeting" (in other words, make sure you're not using either account to boost the other, so one account shouldn't be voting for the other's questions/answers).
I've done the same myself, as I've occasionally had need to post questions regarding specific projects at work that I'd rather not have associated with my main user account, since it uses my real name and a few members of the site know the products that I work on.
Also, what if my co-workers 'mess' with me on stackoverflow?
If they have voting accounts and engage in serial up- or down-voting (which is what I assume you mean by "mess" then this should be automatically detected and reversed.
The system will also highlight multiple accounts that use the same IP (like accounts accessed from work) so this might also appear as "suspicious" activity.